Ramona's backyard is fenced and represented by parallelogram YARD with measures in meters. She installed a 12-meters fence to se
parate a gardening area and a small petting zoo she has for her kids She will have another fence installed in the petting zoo area to separate the goats from the bunnies. She marked the fencing line and it is represented by x in the diagram below 15 12 I x which of the following represents the length of the new fence?
1 answer:
You might be interested in
Options
A. UV = 14 ft and m∠TUV = 45°
B. TU = 26 ft
C. m∠STU = 37° and m∠VTU = 37°
D. ST = 20 ft, UV = 14 ft, and m∠UST = 98°
E. m∠UST = 98° and m ∠TUV = 45°
Answer:
A. UV = 14 ft and m∠TUV = 45°
D. ST = 20 ft, UV = 14 ft, and m∠UST = 98°
Step-by-step explanation:
Given
See attachment for triangle
Required
What proves that: ΔSTU ≅ ΔVTU using SAS
To prove their similarity, we must check the corresponding sides and angles of both triangles
First:
must equal
So:
Next:
UV must equal US.
So:
Also:
ST must equal VT
So:
Lastly
must equal
So:
Hence: Options A and D are correct
Answer:
<em>A) The reference angle should be </em><u><em>,</em></u><em> and the sign of the value should be </em><u><em>negative.</em></u>
Step-by-step explanation:
cos()
Remove full rotations of 2π until the angle is between 0 and 2.
cos()
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.
-cos()
The exact value of cos() is
.
−
Answer:
Step-by-step explanation:
This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is
where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then
a = 5000
If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So
b = 1.035
Our function is
where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.
and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.
Begin by dividing both sides by 5000 to get
and take the natural log of both sides:
The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:
To solve for x, we now divide both sides by ln(1.035):
Do that division on your calculator and get that
x = 11.0 years.
That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)